Digital Signal Processing (DSP) techniques enable an optical transmitter to compensate the impairments affecting optical signal during transmission over a fiber by applying the inverse filter properties of the impairments. These techniques can be applied at two different stages of a transmission system including a transmitter and a receiver respectively transmitting and receiving a light wave signal through a medium, such as an optical fiber.
In the first way, the implementation of the DSP technique is performed at the receiver. Notably, a coherent reception technology enables the receiver to get the information on both phase and amplitude of the received signal. This will allow the DSP to compensate for impairments occurring during transmission before the reception by utilizing appropriately calculated filters. An example of signal equalization in this configuration is illustrated in the non patent literature 1 (NPL1). Furthermore, the equalization based on DSP can be implemented in a signal processor as described in the non patent literature 2 (NPL2).
In another way, the implementation of the DSP technique for equalization is performed at the transmitter. The equalization at the transmitter can be either called pre-distortion, pre-equalization, or pre-compensation depending on the sources. This will allow the DSP to compensate for impairments occurring during transmission after emission of the pre-equalized signal by utilizing appropriately calculated filters. The transmitter emits therefore signal that has been distorted in both amplitude and phase information according to the filters, in order to compensate for the signal with the impairment occurring during transmission in the medium. The non patent literature 3 (NPL3) discloses an example of pre-equalization technique, where both linear impairments like chromatic dispersion (CD) and non-linear impairments like Self Phase Modulation (SPM) are compensated in this manner. The pre-equalization with a DSP enables the transmitter to perform equalization in a more economic way than with a dedicated processor. Alternatively, pre-equalization enables to extend the compensating range of the receiver by adding the compensation range of the transmitter.
In NPL3, the pre-equalized signal is modulated on the optical carrier with an optical IQ modulator (In phase—Quadrature phase modulator), sometimes called Cartesian modulator, vector modulator, Dual Parallel modulator, or nested modulator depending on the sources. In an IQ modulator, the electric signals drive two independent Mach-Zehnder devices, which can be called children Mach-Zehnder Modulators (MZM), or nested MZM depending on the sources. The children MZM modulate the phase and amplitude of the same optical carrier wave. The phase in one of their outputs is relatively delayed by 90 degrees before being recombined. The phase delay between the outputs of the children MZM can be called an angle of quadrature and is ideally 90 degrees, modulo 180 degrees. IQ Modulators enable a chirp-free modulation for the amplitude and phase information in the pre-equalized signal by accessing directly to the I component and the Q component of the light wave signal.
However, it is known that there is a drift of DC (Direct Current) bias in IQ modulators due to variation of the temperature or ageing of the device. There are three types of applied biases, that is, the DC biases of each of the two children MZM and DC bias used to set the angle of quadrature. The drift of DC (Direct Current) bias causes a degradation of the transmitted signal, and therefore results in degradation of the received signal quality or in worst cases the impossibility to decode the received signal. This problem is likely to be revealed in the characterization tests of the modulator at the production stage or at the assembly stage of the transmitter in which the modulator is used. This problem can be solved by using Auto Bias. Control (ABC) circuits, which control the biases of the modulators and compensate for the DC bias change. In this manner, ABC technology can manage the drift of DC bias of IQ modulators, enabling correct modulation in optimal condition.
An example of ABC circuits, which is able to control the DC biases of an IQ modulator driven with multilevel signals in order to generate QAM modulated optical signal, is disclosed in the patent literature 1 (PTL1). The ABC circuit of PTL1 is based on low frequency dither tones to control the DC biases of I and Q components in the children MZM as well as of the angle of quadrature. However, due to the properties of the monitor signal, the optimal DC biases of the children MZM have a periodicity of 2*Vpi, where Vpi is the voltage difference between the biases corresponding to constructive interferences and destructive interferences of the MZM. Similarly, the optimal quadrature angle has a periodicity of 180 degrees. Because of these periodicities, there is an uncertainty of 2*Vpi on the set of DC biases in the children MZM and an uncertainty of 180 degrees of the quadrature angle in the IQ modulator.
Another example of ABC circuits, which is capable of controlling the three biases of an IQ modulator driven with pre-equalized data for pre-equalization of CD, is reported in the non patent literature 4 (NPL4). According to the design of ABC circuits including the example in NPL4, the optimal point for the DC biases of the children MZM is the point of minimum transmission at Vpi, where a phase difference of 180 degrees is created by the DC bias between two arms of the children MZM. The optimal bias point is periodic by 2*Vpi. The angle of quadrature is periodic by 180 degrees. According to these periodicities, there is an uncertainty of 2*Vpi on the set of DC biases in the children MZM and an uncertainty of 180 degrees of the quadrature angle in the IQ modulator.
The output complex field representing the lightwave signal modulated by an IQ modulator can be expressed by the following equation:
                                          E            out                    ⁡                      (                          t              ,                              V                                  bias                  ,                  I                                            ,                              V                                  bias                  ,                  Q                                            ,                              φ                IQ                                      )                          =                                                            E                0                            ⁡                              (                t                )                                      2                    ⁢                                                 [                                                cos                  ⁡                                      (                                                                  π                        2                                            ×                                                                                                                                  V                                                              RF                                ,                                I                                                                                      ⁡                                                          (                              t                              )                                                                                +                                                      V                                                          bias                              ,                              I                                                                                                                                V                          π                                                                                      )                                                  +                                                      ⅇ                                          jφ                      IQ                                                        ×                                      cos                    ⁡                                          (                                                                        π                          2                                                ×                                                                                                                                            V                                                                  RF                                  ,                                  Q                                                                                            ⁡                                                              (                                t                                )                                                                                      +                                                          V                                                              bias                                ,                                Q                                                                                                                                          V                            π                                                                                              )                                                                                  ]                                                          (        1        )            where Eout(t) represents the output complex field, E0(t) is proportional to the complex field of the input lightwave signal of the IQ modulator, Vbias,I represents the DC bias of the I child MZM in the IQ modulator, Vbias,Q represents the DC bias of the Q child MZM in the IQ modulator, φIQ is the angle of quadrature of the IQ modulator, VRF,I(t) represents a driving voltage of I child MZM in the IQ modulator, VRF,Q(t) represents a driving voltage of Q child MZM in the IQ modulator, and Vπ represents a voltage difference between the biases corresponding to constructive interferences and destructive interferences in the children MZM. In this convention, the case Vbias,I=Vπ represents biasing at the null driving point of the child I Mach-Zehnder modulator.
Considering the case of an IQ modulator, with optimal DC biases, the output complex field is as follows:Eout,optimal(t)=Eout(t,Vπ,Vπ,90)  (2)where the DC biases of the MZM children are set at Vpi and the angle of quadrature of the IQ modulator is set at 90 degrees.
Referring to the ambiguity of the optimal DC biases set by an ABC circuit controlling the IQ modulator, the following cases are also optimal considering the DC biases of the IQ modulator:Eout(t,3×Vπ,Vπ,90)=−Eout,optimal(t) (Opposite of the complex conjugate of (2)),  (3)Eout(t,Vπ,3×Vπ,90)=Eout,optimal(t) (Complex conjugate of (2)),  (4)Eout(t,Vπ,Vπ,270)=Eout,optimal(t) (Complex conjugate of (2)),  (5)
In the case of modulation of signal with QPSK or QAM format with the IQ modulator, depending on the DC bias set by the ABC circuit and considering the uncertainty of the set DC bias, the output field is susceptible to a reference output filed such as its opposite, its complex conjugate, or the opposite of its complex conjugate. The uncertainty of the state can be easily resolved at the receiver after symbol decision using training pattern or framing information.